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Cubes and Cuboids Questions and Answers

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Question 16 - Bancrofts School 11 Plus Maths Sample Paper 2 2021

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Sevenoaks School Year 7 Entrance Exam 2020 - Question 17

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Question 16 - The Manchester Grammer School 11 Plus Entrance Examination 2007

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Question 30 - Haberdashers Askes Boys School HABS - 11 Plus Entrance Examination 2008

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Group 2 Maths 2017 - Question 29

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Sevenoaks School Year 7 Sample Paper 2013 Question 14

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Chigwell School - 11 Plus Maths Specimen Paper 2020 entry Question 27

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Queens’ School - Maths Familiarisation Paper Question 13

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ISEB 11 Plus Maths 2009-10 Practice Paper Question 27

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CSSE Maths 2016 Entry Question 20

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Sevenoaks School Year 7 Sample Paper 2016 Question 17

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Sevenoaks School Year 7 Sample Paper 2014 Question 12

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Bancroft’s School - Sample 11+ Maths Paper 2020 Question 29, Geometry, 3D Shapes, Volume, Cubes and Cuboids

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Bancroft’s School - Sample 11+ Maths Paper 2020 Question 25, Geometry, Cubes and Cuboids, Logical Problems

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Properties of Cubes and Cuboids for 11 plus Exam

1. Properties of Cube

Cube: The cube is one of the simplest three-dimensional shapes with the dimensions length, width, and height all of the same size. It has six-square faces, eight vertices, and twelve edges. 

Some real-life examples of cubes are Rubik’s cube, 6-sided dice, etc.

11+ Topicwise Cubes and Cuboids Article image 1

2. Properties of Cuboid

Cuboids: A cuboid is a three-dimensional shape with the dimensions as length, width and height. It has six rectangular faces, eight vertices and twelve edges.

Some simple real-life examples of cuboids are bricks, lunch box, etc.

11+ Topicwise Cubes and Cuboids Article image 2

3. Area and Volume formulas of Cube and Cuboid

Cube 

11+ Topicwise Cubes and Cuboids Article image 3

Side of the cube is a.

Surface area of the cube = 6a²

Volume of the cube = a³

Cuboid 

11+ Topicwise Cubes and Cuboids Article image 4

l, w and h are the dimensions of cuboid

Surface area of cuboid = 2(lw+wh+lh)

Volume of cuboid = l × h

3.1 Example Question on Area and Volume of Cube

Surface area of a cube is 96 cm². Work out the edge and volume of this cube.

Solution :

Surface area of a cube = 6a²

                               96 = 6a²   

                               a² = 96 ÷ 6

                               a² = 16

                          a × a = 4 × 4

                                a = 4 cm

Side of the cube is 4 cm

Volume of a cube = a³

                             = (4)³

                             = 4 × 4 × 4

                             = 64 cm³

3.2 Example Question on Area and Volume of Cuboid

Calculate the volume and surface area of the cuboid shown below.

11+ Topicwise Cubes and Cuboids Article image 5

Solution:

Length of Cuboid (l) =  20 mm

Width of Cuboid  (w) =  4 mm

Height of Cuboid (h) =  12 mm

Volume of Cuboid = l ×w × h

                             = 20 × 4 × 12

                             = 960 mm³

Surface area of cuboid =  2(lw + wh + lh)

                                     = 2 (20 × 4 + 4 × 12 + 12 × 20)

                                     = 2(80 + 48 + 240)

                                     = 368 mm²

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